Question

On a highway curve with a radius of 46 meters, the maximum force of static friction that can act on a 1,200 kg car going around the curve is 7,500 Newtons. What speed limit should be posted for the curve so that cars can negotiate it safely

Answer 1

Answer:

$v\approx 16.956\,\frac{m}{s}$

Explanation:

The motion of the vehicule on a highway curve can be modelled by the following equation of equilibrium:

$\Sigma F = f = m\cdot \frac{v^{2}}{R}$

The maximum speed is:

$v = \sqrt{\frac{f\cdot R}{m} }$

$v = \sqrt{\frac{(7500\,N)\cdot (46\,m)}{1200\,kg} }$

$v\approx 16.956\,\frac{m}{s}$